There are numerous known devices for carrying and cooling beverage containers. In U.S. Pat. No. 3,998,072 to Shaw (December 1976) a portable wine cooler case has flasks of coolant that surround the body of a bottle. However, the case leaves the neck of the body unprotected. In other carrying cases such as U.S. Pat. No. 5,564,583 to Kelley et al. (October 1996), a cover does protect the neck of the beverage container, but the case does not conform to the shape of the neck. That leaves the carrying case unnecessarily bulky, and allows some types of bottles to shift unnecessarily within the case. Accordingly, there is still a need to provide improved beverage container carrying cases.